Final answer:
The calculation {∑_{n=1}^{[infinity]} n^{2} sin(1/n^{2}+1)} is a complex series sum combining a power and a trigonometric function. Solution to this would often require advanced mathematical knowledge or calculus with specifics like convergence test or a particular manipulation.
Step-by-step explanation:
The equation presented, ∑_{n=1}^{[infinity]} n^{2} sin(1/n^{2}+1), is a series sum that combines a power function (n^2), and a trigonometric function (sin(1/n^2+1)). This arrangement is quite complex and would often be encountered in advanced mathematical studies or calculus. Unfortunately without additional context or instruction, we can't produce a concrete answer. Additional information would be required such as the application of a specific test for convergence or a hint towards a manipulation that would make the series easier to handle.
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